Trigonometry Examples

${0.8}^{x} = 5$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({0.8}^{x}) = \ln (5)$

Step 2

Expand $\ln ({0.8}^{x})$ by moving $x$ outside the logarithm.

$x \ln (0.8) = \ln (5)$

Step 3

Divide each term in $x \ln (0.8) = \ln (5)$ by $\ln (0.8)$ and simplify.

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Step 3.1

Divide each term in $x \ln (0.8) = \ln (5)$ by $\ln (0.8)$ .

$\frac{x \ln (0.8)}{\ln (0.8)} = \frac{\ln (5)}{\ln (0.8)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\ln (0.8)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \ln (0.8)}{\ln (0.8)} = \frac{\ln (5)}{\ln (0.8)}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (5)}{\ln (0.8)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (5)}{\ln (0.8)}$

Decimal Form:

$x = - 7.21256743 \dots$